Class VARMAXModel

  • Direct Known Subclasses:
    VARXModel

    public class VARMAXModel
    extends VARIMAXModel
    The VARMAX model (ARMA model with eXogenous inputs) is a generalization of the ARMA model by incorporating exogenous variables. Xt is an ARMAX(p, q) process, for which \[ X_t = \mu + \sum \phi_i X_{t-i} + \sum \theta_j \epsilon_{t-j} + \psi' D_t + \epsilon_t, \] Xt, μ and εt are n-dimensional vectors. The (n * n) matrices \({\phi_i}\) and \({\theta_j}\) are the AR and MA coefficients respectively. Dt is an (m * 1) vector which contains all exogenous variables at time t (excluding the intercept term), and its coefficients are represented by an (n * m) matrix ψ.
    See Also:
    Wikipedia: Autoregressive moving average model - Generalizations
    • Constructor Detail

      • VARMAXModel

        public VARMAXModel​(Vector mu,
                           Matrix[] phi,
                           Matrix[] theta,
                           Matrix psi,
                           Matrix sigma)
        Construct a multivariate ARMAX model.
        Parameters:
        mu - the intercept (constant) vector
        phi - the AR coefficients (excluding the initial 1); null if no AR coefficient
        theta - the MA coefficients (excluding the initial 1); null if no MA coefficient
        psi - the coefficients of the deterministic terms (excluding the intercept term)
        sigma - the white noise covariance matrix
      • VARMAXModel

        public VARMAXModel​(Vector mu,
                           Matrix[] phi,
                           Matrix[] theta,
                           Matrix psi)
        Construct a multivariate ARMAX model with unit variance.
        Parameters:
        mu - the intercept (constant) vector
        phi - the AR coefficients (excluding the initial 1); null if no AR coefficient
        theta - the MA coefficients (excluding the initial 1); null if no MA coefficient
        psi - the coefficients of the deterministic terms (excluding the intercept term)
      • VARMAXModel

        public VARMAXModel​(Matrix[] phi,
                           Matrix[] theta,
                           Matrix psi,
                           Matrix sigma)
        Construct a multivariate ARMAX model with zero-intercept (mu).
        Parameters:
        phi - the AR coefficients (excluding the initial 1); null if no AR coefficient
        theta - the MA coefficients (excluding the initial 1); null if no MA coefficient
        psi - the coefficients of the deterministic terms (excluding the intercept term)
        sigma - the white noise covariance matrix
      • VARMAXModel

        public VARMAXModel​(Matrix[] phi,
                           Matrix[] theta,
                           Matrix psi)
        Construct a multivariate ARMAX model with unit variance and zero-intercept (mu).
        Parameters:
        phi - the AR coefficients (excluding the initial 1); null if no AR coefficient
        theta - the MA coefficients (excluding the initial 1); null if no MA coefficient
        psi - the coefficients of the deterministic terms (excluding the intercept term)
      • VARMAXModel

        public VARMAXModel​(ARMAXModel model)
        Construct a multivariate model from a univariate ARMAX model.
        Parameters:
        model - a univariate ARIMA model
      • VARMAXModel

        public VARMAXModel​(VARMAXModel that)
        Copy constructor.
        Parameters:
        that - a multivariate ARMAX model
    • Method Detail

      • armaxMean

        public Matrix armaxMean​(Matrix arLags,
                                Matrix maLags,
                                Vector exVar)
        Compute the multivariate ARMAX conditional mean.
        Parameters:
        arLags - the AR lags
        maLags - the MA lags
        exVar - the exogenous variables
        Returns:
        the conditional mean